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URGENT help required, OG 13 questions

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URGENT help required, OG 13 questions [#permalink] New post 08 Apr 2013, 08:57
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Q1)A ladder of a fire truck is elevated to an angle of 60 degrees and extended to a length of 70 feet. if the base of the ladder is 7 fet above the ground, how many feet above the ground does the ladder reach?
a) 35
b) 42
c) 35 \sqrt{3}
d) 7+ 35\sqrt{3}
e) 7+42\sqrt{3}


Q2) the price of lunch for 15 people was $207.00, including a 15% gratuity for service. What was the average price per person EXCLUDING the gratuity?
a)11.73
b)12
c)13.8
d)14
e)15.87

Q3) for any psitive integer n, the sum fo the first n positive integers equals [n(n+1)]/2. what si the sum of all the even integers betwen 99 and 301?
a) 10,100
b) 20,200
c) 22,650
d) 40,000
e) 45,150

Q4)Last year the price per share of stock X increased by k percent and the earnings per share of stock X increased by m percent, where k is greater than m. By what percent is the ratio of price per share to the earnings per share increase, in terms of k and m?
a) k/m
b) k-m
c) [100(k-m)]/ 100+k
d) [100(k-m)]/[100+m]
e) [100(k-m)/(100+k+m)

Q5) of the 300 subjects who participated in an experiment using virtual reality therapy to reduce their fear of heights, 40% experienced sweaty palms, 30% experienced vomiting, and 75% experienced dizziness. If all the subjects experienced at least one of these effects, and 35 % of the subjects experienced exactly two of these effects, how may of the subjects experienced only one of these effects?
a)105
b)125
c)130
d)180
e)195

Q6) if m>0 and x is m percent of y, then in terms of m, y is what percent of x?
a)100m
b)1/(100m)
c) 1/m
d) 10/m
e) 10,000/m

Q7) Seven pieces if rope have an average of length of 68 cmand median length of 84 cm. if the length f the longest piece of rope is 14 cm more than 4 times the length of the shortest piece of rope, what si maximum possible length , in cm, of the longest piece of rope?
a)82
b)118
c)120
d)134
e)152

Q8) [0.99999999/1.0001]- [0.99999991/1.0003]=
a) 10^-8
b) 3(10^-8)
c) 3 (10^-4)
d) 2(10^-4)
e) 10^-4

Q9) List T consists of 30 positive decimals, none of which is an integer, and the sum of 30 decimals is S. the estimated sum of the 30 decimals, E is defined as follows. Each decimal in T whose tenths digit is even is rounded up to the nearest integer, and each decimal in T whose tenths digit is odd is rounded down to the nearest integer; E is the sum of the resulting integers. If 1/3 of the decimals in T have a tenths digit that is even, which of the following is a possible value of E-S?
1. -16
2. 6
3.10

A) 1 only
B) 1 and 2 only
C) 1 and 3 only
D) 2 and 3 only
E) 1,2 and 3

Last edited by bb on 13 Apr 2013, 00:18, edited 2 times in total.
Edited the question.
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Re: URGENT help required, OG 13 questions [#permalink] New post 08 Apr 2013, 09:05
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That's a lot of questions !

Q1)A ladder of a fire truck is elevated to an angle of 60 degrees and extended to a length of 70 feet. if the base of the ladder is 7 fet above the ground, how many feet above the ground does the ladder reach?

The ladder forms a 30 60 90, triangle which has dimentions 1x \sqrt{3} 2, the hip is 70=2x so x=35, the H of the triangle is 35\sqrt{3}, but the ladder is 7 feet from the ground => it reaches 7+35\sqrt{2}

IMO D
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Re: URGENT help required, OG 13 questions [#permalink] New post 08 Apr 2013, 09:08
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Q2) the price of lunch for 15 people was $207.00, including a 15% gratuity for service. What was the average price per person EXCLUDING the gratuity?

X=price
x+0.15x=207, 1.15x=207, x=\frac{207}{1.15}, x=180
They paid 180 $ tot, so \frac{180}{15}=12 each
IMO B
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Re: URGENT help required, OG 13 questions [#permalink] New post 08 Apr 2013, 09:14
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Q3) for any psitive integer n, the sum fo the first n positive integers equals [n(n+1)]/2. what si the sum of all the even integers betwen 99 and 301?

100 ... 200 ... 300
Between 200 and 100 there are 200/2-100/2+1=51 even integers
Between 300 and 200 there are 300/2-200/2+1=51 even integers
But we counted 200 twice, so tot even entegers = 51+51-1=101.
As you can see their mean is 200
So tot sum is200*101=20200
IMO B
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Re: URGENT help required, OG 13 questions [#permalink] New post 08 Apr 2013, 09:18
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Quote:
Q3) for any psitive integer n, the sum fo the first n positive integers equals [n(n+1)]/2. what si the sum of all the even integers betwen 99 and 301?
a) 10,100
b) 20,200
c) 22,650
d) 40,000
e) 45,150


Sum of all even integers is Avg. * count of numbers in series 99 - 301

Avg = first + last / 2 = 100 + 300 / 2 = 200
count of numbers in the series = 300 - 100 / 2 + 1 = 101

Sum = 200 * 101 = 20200. Answer is B

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Re: URGENT help required, OG 13 questions [#permalink] New post 08 Apr 2013, 09:22
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Q6) if m>0 and x is m percent of y, then in terms of m, y is what percent of x?
a)100m
b)1/(100m)
c) 1/m
d) 10/m
e) 10,000/m


x = (m/100)*y
y/x = (y/m*y/100)*100 = 10,000/m .

Answer is E

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Re: URGENT help required, OG 13 questions [#permalink] New post 08 Apr 2013, 09:24
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Q5) of the 300 subjects who participated in an experiment using virtual reality therapy to reduce their fear of heights, 40% experienced sweaty palms, 30% experienced vomiting, and 75% experienced dizziness. If all the subjects experienced at least one of these effects, and 35 % of the subjects experienced exactly two of these effects, how may of the subjects experienced only one of these effects?

Use the formula : Tot = S+V+D-(two)+2(three) = 100

300 = 120 + 90 + 225 - 105 - 2*(three)
so 15 had all three

To see the number of subjects with 1 effect:
S+V+D-2*two-3*three = 435 - 210 - 45 = 180

Refer to this formulae-for-3-overlapping-sets-69014.html
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Re: URGENT help required, OG 13 questions [#permalink] New post 08 Apr 2013, 09:28
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Q6) if m>0 and x is m percent of y, then in terms of m, y is what percent of x?

x= \frac{m}{100}y
100x=m*y
y= \frac{100}{m}x
y= (10000/m)/100 (of) x
y = \frac{10,000}{m}
IMO E
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Re: URGENT help required, OG 13 questions [#permalink] New post 08 Apr 2013, 09:41
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Q6) if m>0 and x is m percent of y, then in terms of m, y is what percent of x?
a)100m
b)1/(100m)
c) 1/m
d) 10/m
e) 10,000/m

Assume m=100%. Thus x=y, only E gives the answer as 100%.

E.
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Re: URGENT help required, OG 13 questions [#permalink] New post 08 Apr 2013, 09:42
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Free OG video explanations here: http://www.gmatquantum.com/og13th/

Thanks to gmatclub member dabral
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Re: URGENT help required, OG 13 questions [#permalink] New post 08 Apr 2013, 09:45
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Q.6

x = my/100
we have to find 100y/x = ?

y/x = 100/m

Multiple both sides by 100

100y/x = 10000 / m

hence E is the answer
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Re: URGENT help required, OG 13 questions [#permalink] New post 08 Apr 2013, 09:45
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Q3) for any psitive integer n, the sum fo the first n positive integers equals [n(n+1)]/2. what si the sum of all the even integers betwen 99 and 301?
a) 10,100
b) 20,200
c) 22,650
d) 40,000
e) 45,150

No of even terms between 99 and 301-->(300-100)/2 +1 = 101. Thus the sum = 101/2 * (100+300) = 200*101 = 20200
B.
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Re: URGENT help required, OG 13 questions [#permalink] New post 08 Apr 2013, 09:47
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Q5) of the 300 subjects who participated in an experiment using virtual reality therapy to reduce their fear of heights, 40% experienced sweaty palms, 30% experienced vomiting, and 75% experienced dizziness. If all the subjects experienced at least one of these effects, and 35 % of the subjects experienced exactly two of these effects, how may of the subjects experienced only one of these effects?


Let x represent subjects who experienced only sweaty palms
Let y represent subjects who experienced only vomiting
Let z represent subjects who experienced only dizziness
Let a represent subjects who experienced only sweaty palms and dizziness
Let b represent subjects who experienced only sweaty palms and vomiting
Let c represent subjects who experienced only vomiting and dizziness
Let d represent subjects who experienced vomiting, sweaty palms, and dizziness


x+a+b + d = 120
y+b+c +d = 90
z+a+c +d = 225

x+y+z +2 (a+b+c) - 3d = 120 + 90 + 225 - 105 - 3*15 = 180

Answer : D

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Re: URGENT help required, OG 13 questions [#permalink] New post 08 Apr 2013, 10:05
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Q7. Mean of 7 wood pieces = 68
therefore total length of 7 pieces = 68 * 7 = 476 cms

Median of 7 pieces = 84
To have the 7th piece of maximum length we must have 4th, 5th, 6th piece = median length of 84 and 1st, 2nd and 3rd piece = smallest wood length.

1st (SMALLEST) --- 2nd (SMALLEST) --- 3rd (SMALLEST) --- 4th (MEDIAN) --- 5th (MEDIAN) --- 6th (MEDIAN) --- 7th (LONGEST)

Sum (4th, 5th and 6th) = 84 * 3 = 252 cms
Let smallest wood piece be x cms
Sum (1st, 2nd and 3rd) = 3x
Longest piece = 4*smallest + 14

therefore 252 + 3x + 4x + 14 = 476
x = 30

hence longest piece = 134 cms
Ans D
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Re: URGENT help required, OG 13 questions [#permalink] New post 08 Apr 2013, 10:12
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Q8. lets remove decimals first from both the denominators
9999 / 10001 - 9999 / 10003
=> {(10003 - 10001) * 9999} / 10^8
=> 2 * 9999 / 10^4

since 9999 is approx 10000 or 10^4
we can wrire 2 * 10^4 / 10^8 or 2 * 10^(-4)

hence D is answer
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Re: URGENT help required, OG 13 questions [#permalink] New post 08 Apr 2013, 10:15
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Q5. 100 = 40 + 30 + 75 - 35 - 2(all three)
All three = 5%

therefore 2 effects + 3 effects = 40%
hence % who only experienced one fo the effects = 60%
60% of 300 = 180 students
hence D
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Re: URGENT help required, OG 13 questions [#permalink] New post 08 Apr 2013, 10:19
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Q9) Let the 30 decimals be d1, d2, d3,... d30 and corresponding 30 integers are i1, i2, i3,... i30

The integer set will have 1/3 of the numbers will be higher by 1 from decimal set and 2/3 of the numbers will be lower by 1 from decimal set.

E - S = 1/3S - 2/3S - S = -4/3S. Looking at the options only -16 can be an integer result of -4/3S

Hence the answer is A - I only

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Last edited by nt2010 on 08 Apr 2013, 10:21, edited 1 time in total.
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Re: URGENT help required, OG 13 questions [#permalink] New post 08 Apr 2013, 10:20
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Q2. 1.15x = 207
x = 180
cost of 15 people = 180 (without gratuity)
cost per person = 180 / 15 = 12
hence B
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Re: URGENT help required, OG 13 questions [#permalink] New post 08 Apr 2013, 10:23
Q3. sum of evenly spaced sets = avg of 1st and last term * # of terms

Avg of first and last = avg (100,300) = 200
# of terms = {(300 - 100)/ 2} + 1 = 101 terms

hence sum = 200 * 101 = 20200
Ans B
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Re: URGENT help required, OG 13 questions [#permalink] New post 08 Apr 2013, 10:29
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Q2) the price of lunch for 15 people was $207.00, including a 15% gratuity for service. What was the average price per person EXCLUDING the gratuity?
a)11.73
b)12
c)13.8
d)14
e)15.87

Here the word EXCLUDING is used.
So 0.15 * 207=$31.05
Therefore,207-31.05=$175.95

So the average cost per person=175.75/15=11.73
So ans should be (A) IMO.
Re: URGENT help required, OG 13 questions   [#permalink] 08 Apr 2013, 10:29
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